Hello, I am trying to make a "game" that will take calculus integration formula and generate three dimensional pictures of the results.

My three main questions are:
1. There is no built-in integration formula so should I just make a picture that resembles integration and include the already integrated lines of math for actual calculations? In other words, the user will see the integration symbol but the math behind the scenes will be already integrated? Or is there an integration formula I am unaware of?

2. I dont see any clear cut way of making a 2D graph or assigning numbers to the graph, I was thinking of making a picture of a graph but it would be static, say 0-10 on the X and Y plane. I would LOVE to be able to alter the dimensions of the graph and in fact I think it may be necessary but there is no "drag and drop" graph from the toolbar... what are my options?

3. For integration of 2D graphs that give 3D objects, such as the shell method for a parabola wrapped around the Y-axis, where should the object output to (the form background perhaps?)- and I would love to be able to rotate it using the mouse. (click and drag to rotate 3D object). again there is no tool for this, I am wondering even quite how to begin such a thing.

In regard to question #1:
Take a look at the Symbol font in the Windows Character Map utility.
It has the integration symbol as well as some other greek and math symbols.
It might do in a pinch.
There are other latex fonts out there but not many truetype with free distribution.
I recommend you create the font text symbols in a memory DC amd bitblt them where you need them in the equation (also works for text labels of graphs). http://www.vb-helper.com/howto_memory_bitmap_text.html